Nuprl Lemma : first-interface-implies-prior-interface
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)].
∀[e:E]. ↑e ∈b prior(Y) supposing ↑e ∈b prior(X) supposing ∀e:E. ((↑e ∈b X) ⇒ (¬↑e ∈b prior(X)) ⇒ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
es-E-interface: E(X),
es-locl: (e <loc e'),
rev_implies: P ⇐ Q,
cand: A c∧ B
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)].
\mforall{}[e:E]. \muparrow{}e \mmember{}\msubb{} prior(Y) supposing \muparrow{}e \mmember{}\msubb{} prior(X)
supposing \mforall{}e:E. ((\muparrow{}e \mmember{}\msubb{} X) {}\mRightarrow{} (\mneg{}\muparrow{}e \mmember{}\msubb{} prior(X)) {}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} Y))
Date html generated:
2016_05_16-PM-11_55_45
Last ObjectModification:
2016_01_17-PM-07_00_39
Theory : event-ordering
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